2.1694   ODE No. 1694

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

\[ y(x) y''(x)-a=0 \] Mathematica : cpu = 0.134934 (sec), leaf count = 115

\[\left \{\left \{y(x)\to \exp \left (\frac {-2 a \text {erf}^{-1}\left (-i \sqrt {\frac {2}{\pi }} \sqrt {a e^{\frac {c_1}{a}} (x+c_2){}^2}\right ){}^2-c_1}{2 a}\right )\right \},\left \{y(x)\to \exp \left (\frac {-2 a \text {erf}^{-1}\left (i \sqrt {\frac {2}{\pi }} \sqrt {a e^{\frac {c_1}{a}} (x+c_2){}^2}\right ){}^2-c_1}{2 a}\right )\right \}\right \}\] Maple : cpu = 1.28 (sec), leaf count = 54

\[\left \{-c_{2}-x +\int _{}^{y \left (x \right )}\frac {1}{\sqrt {-2 c_{1} a +2 a \ln \left (\textit {\_a} \right )}}d \textit {\_a} = 0, -c_{2}-x +\int _{}^{y \left (x \right )}-\frac {1}{\sqrt {-2 \left (c_{1}-\ln \left (\textit {\_a} \right )\right ) a}}d \textit {\_a} = 0\right \}\]